A378437 Dirichlet inverse of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

1, -1, -1, 0, -1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, -1, 1, 1, -1, -2, 0, 1, 0, -1, -1, -2, -1, 0, 1, 1, 1, -2, -1, 1, 1, -1, -1, -1, -1, 0, 0, 1, -1, -2, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, -26, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, -14, -1, 1, 0, 0, 1, 0, -1, -1, 0, 1, -1, -19, 1, 1, 1, -1, -1, -17, 1, 0, 1, 1, 1

Offset

1,24

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A033630(n/d) * a(d).

Prog

(PARI)
A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
memoA378437 = Map();
A378437(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378437, n, &v), v, v = -sumdiv(n, d, if(d<n, A033630(n/d)*A378437(d), 0)); mapput(memoA378437, n, v); (v)));

Crossrefs

Cf. A033630, A378438 (Möbius transform).

Sequence in context: A108234 A324572 A153148 * A091830 A029427 A353506

Adjacent sequences: A378434 A378435 A378436 * A378438 A378439 A378440

Keyword

sign

Author

Antti Karttunen, Nov 26 2024

Status

approved